These steps lead to the following calculations to determine the probability of
payment being before notice:
Probabilities
Relevant probabilities are as follows:
Notice is given in the 23 minute period
23/30
Payment is made in the 23 minute period
23/60
Both notice and payment are in this period
(23/30) x (23/60)
Half these cases payment will be before notice
1/2
Calculation
Probability that payment is made before notice is given is one half the
probability that both notice and payment are in the 23 minute period. The
formula is:
(23/30) x (23/60) x (1/2)
=
529/3600
=
0.147 (approximately)
=
14.7% (approximately)
Conclusion
The probability that payment is given before notice is approximately 14.7%.
Comment
The reasoning in this case is open to criticism. In the case there was lack of
direct evidence. This is not the equivalent of all outcomes being equally likely
which is the precondition for classical probability.
Collins Case
In People v
Collins
an elderly lady in Los Angeles was knocked down and
robbed.
620
Bystanders said the assailants were a caucasian female with blond
hair tied in a ponytail and black male with a beard
and moustache. They
escaped in a yellow motor car. The two defendants in the case fell within these
broad
descriptions. However, the victim
but could not conclusively identify
them as the assailants. In an endeavour to prove their guilt the prosecutor used
a mathematics professor to estimate
the probability that this couple could or
could not be the guilty party. At first instance both defendants were convicted.
On appeal, the conviction was overturned. The court criticised the way in
which probability had been used, because it failed to take into account the
probable dependencies between the characteristics, for example, bearded men
commonly sport moustaches. Other criticism by academics was that it was an
620
People v Collins, 438 P.2d 33 (Cal. 1968)
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